Dynamic Monitoring and Vibration Analysis of Ancient Bridges by Ground-Based Microwave Interferometry and the ESMD Method

In this paper, we propose to conduct a dynamic monitoring and vibration analysis of ancient bridges by means of ground-based microwave interferometry and the extreme-point symmetric mode decomposition (ESMD) method. Ground-based microwave interferometry, a novel non-contact technology with a high accuracy, is used to acquire dynamic time series displacements with environmental excitation factors and a transient load with a car, respectively. The ESMD method, a new alternative to the Hilbert-Huang transform (HHT), is adopted to conduct the instantaneous vibration analysis of Zhaozhou Bridge. Firstly, a series of intrinsic mode functions (IMFs) are obtained together with an optimal adaptive global mean (AGM) curve by using a mode symmetric about the maxima and minima points. Secondly, the instantaneous frequency of each IMF is obtained by the use of a direct interpolation algorithm, which can reconcile the conflict between the period and the frequency for the traditional time-frequency analysis methods. As a representative case, Zhaozhou Bridge, a well-known Chinese ancient bridge constructed more than 1400 years ago, is studied in detail. Four kinds of dynamic time series displacements—two of them acquired by considering only environmental excitation factors for the mid-span and 1/4-span points and the others obtained with the transient load of a car for the mid-span and 1/4-span points—are selected to pursue a comparison of the decomposed IMFs and the instantaneous frequencies to perform the instantaneous vibration analysis of Zhaozhou Bridge. By comparing the results obtained with HHT for the decomposed IMFs and the instantaneous frequencies, the results show that the proposed method has a powerful ability to evaluate the instantaneous dynamic response of ancient bridges

Dynamic Monitoring and Vibration Analysis of Ancient Bridges by Ground-Based Microwave Interferometry and the ESMD Method

In this paper, we propose to conduct a dynamic monitoring and vibration analysis of ancient bridges by means of ground-based microwave interferometry and the extreme-point symmetric mode decomposition (ESMD) method. Ground-based microwave interferometry, a novel non-contact technology with a high accuracy, is used to acquire dynamic time series displacements with environmental excitation factors and a transient load with a car, respectively. The ESMD method, a new alternative to the Hilbert-Huang transform (HHT), is adopted to conduct the instantaneous vibration analysis of Zhaozhou Bridge. Firstly, a series of intrinsic mode functions (IMFs) are obtained together with an optimal adaptive global mean (AGM) curve by using a mode symmetric about the maxima and minima points. Secondly, the instantaneous frequency of each IMF is obtained by the use of a direct interpolation algorithm, which can reconcile the conflict between the period and the frequency for the traditional time-frequency analysis methods. As a representative case, Zhaozhou Bridge, a well-known Chinese ancient bridge constructed more than 1400 years ago, is studied in detail. Four kinds of dynamic time series displacements—two of them acquired by considering only environmental excitation factors for the mid-span and 1/4-span points and the others obtained with the transient load of a car for the mid-span and 1/4-span points—are selected to pursue a comparison of the decomposed IMFs and the instantaneous frequencies to perform the instantaneous vibration analysis of Zhaozhou Bridge. By comparing the results obtained with HHT for the decomposed IMFs and the instantaneous frequencies, the results show that the proposed method has a powerful ability to evaluate the instantaneous dynamic response of ancient bridges